The perception of color in human vision results from combinations of spectral distributions of light radiation being sensed by red, green and blue photoreceptors on the retina. The photoreceptors provide corresponding encoded signals, referred to as a color stimulus, to the brain which interprets the signals causing the perception of color. However, different spectral distributions can result in similar encoded signals, a phenomenon known as metamerism. Many color reproduction systems take advantage of the principle of metamerism to present spectral distributions to the retina that result in the perception of a particular desired color, even if the original spectral distribution was different to that in the reproduction.
In color science the encoded signals are referrred to as tristimulus values, being the amounts of the three primary colors that specify the color stimulus. The Commission Internationale de l'Eclairage (CIE) has standardized many aspects of color science and the 1931 CIE tristimulus values are called X, Y, and Z, respectively. The need for a uniform color space led to a number of non-linear transformations of the CIE 1931 XYZ space and finally resulted in the specification of one of these transformations as the CIE 1976 (L* a* b*) color space. The L* coordinate represents lightness and extends along an axis from 0 (black) to 100 (white). The other two coordinates a* and b* represent redness-greenness and yellowness-blueness respectively. Samples for which a*=b*=0 are achromatic and thus the L*-axis represents the achromatic scale of grays from black to white.
In color reproduction systems color images are generally reproduced using a combination of three or more color components such as Cyan, Magenta and Yellow (CMY) or Red, Green and Blue (RGB). For example, in color printing, Black (K) is also often added to the CMY set to improve rendering of dark tones (CMYK). Advances in digital imaging and computers have lead to a proliferation in the availability of digital images and corresponding advances in color printing have made possible the accurate representation of a real scene using a digital image.
Color management is a significant challenge, particularly in the printing industry wherein the need for precise rendering of color is well established and tools that assist a printer in achieving such precision have been available for some time. Color printing processes involve a range of different output devices including, but not limited to, offset lithographic, flexographic, and gravure printing presses, inkjet printers, xerographic printers, laser printers etc. In particular, matching a color proof sheet to the press sheet has always been a key objective, since the customer typically approves the color proof and will not accept a final print job that does not match the signed-off color proof.
It is well established that particular output devices have a color gamut determined by the colorants used to reproduce an image (e.g. inks on a printer). The color gamut demarcates that portion of color space in which a color expressing system can produce colors. The color gamut may be defined by a matrix of values defining the boundaries of the demarcated portion of color space.
In managing color it is very useful to know the limits or boundaries of the color gamut for a particular device. These limits are typically defined in color space by a gamut boundary descriptor (GBD). The GBD can be used to predict the range of achievable colors for a given set of colorants. Where the GBD indicates that colors in an original image are not achievable on an output device; steps may be taken to bring “out-of-gamut” colors “into gamut”. Such steps may include a gamut mapping process that maps out-of-gamut colors to colors on or within the GBD. The particular gamut mapping process used may depend on the image type or viewing conditions and will typically involve repositioning out-of-gamut colors on or within the gamut boundary and may also involve applying tonal correction to colors that were on or inside the boundary to preserve overall tonal graduation.
A color gamut may be constructed by considering all possible interactions between the available colorants. Invariably, as the number of colorants is increased, the construction of a color gamut becomes much more complex and computationally inefficient due to the rapidly increasing number of possible interactions between colorants. Earlier color gamut construction techniques have often traded off speed for accuracy and vice-versa. Convex Hull based algorithms, such as that described in published U.S. patent application Ser. No. 2002/0140701A1 to Guyler, approximate the shape of the color gamut by operating on a set of points, which are derived from the measurement of color patches. It should be noted that in those parts of the color gamut where the boundary assumes a concave curvature, the convex hull description results in significant error.
Other techniques that employ more rigorous boundary detection algorithms are often quite slow. This results from the need to for matrix inversion operations on the forward model using such techniques as Newton-Raphson or simplex optimization to iteratively search for solutions. The forward model is a mathematical construct that relates ink combinations to color. In addition, these techniques are prone to converging on local minima, thereby creating inaccuracies.
U.S. Pat. No. 5,563,724 describes the characterization of a seven-ink printing process by decomposing the problem into six four-ink groupings. A separate subgamut is constructed from each of the six forward models. A super gamut is then constructed from the six subgamuts. A disadvantage of the process is that it is limited to inking each color with a maximum of four inks.
Accordingly there is a need for a system and method for constructing a color gamut boundary for a set of N-colorants, that mitigates some of the above disadvantages.